# Temporal Transferability of Pine Forest Attributes Modeling Using Low-Density Airborne Laser Scanning Data

^{1}

^{2}

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^{5}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Forest Inventory Data

^{−1}considering those with larger dbh.

#### 2.3. Inventories Updating and Stand Variable Computation

#### 2.4. ALS Data and Processing

#### 2.5. Modeling of Forest Stand Attributes and Temporal Tranferability Assessment

#### 2.5.1. Variable Selection and Attributes Modeling Using the Indirect Approach

#### 2.5.2. Assessment of Temporal Transferability by Applying a Direct Approach

## 3. Results

#### 3.1. Field Plot Computation

^{2}of 0.93.

_{0}and D

_{0}are the dominant height and dominant diameter, as defined in Section 2.3.

^{−1}and G ranges from 0.82 to 58.89 m

^{2}ha

^{−1}, presenting also a variety of diameters, from 9.21 to 47.96 cm. V and W data show also a high range of values with a standard deviation in both cases higher than 60 tons ha

^{−1}. The high range and standard deviation values of the forest inventory attributes show the variability that characterizes Aleppo pine forest in Aragón region.

^{−1}, which may be caused by tree growth, resulting in an average of N change of 10.56 stems ha

^{−1}·G shows average values of change of 2.55 m

^{2}ha

^{−1}and Dg and Do changes range from around 1.73 to 2.13 cm of growth, respectively. Ho values show an average increment of 0.62 m, ranging from 0.35 to 1.89 m. V and W changes show similar values ranging from around 2.00 to 50.00 tons ha

^{−1}with average values around 17.00 tons ha

^{−1}.

#### 3.2. Variable Selection

#### 3.3. Indirect Approach

#### 3.4. Direct Approach

^{2}ranges from 0.64 to 0.93 within the different stand attributes. As it is shown in Table 5, models are transferable. In fact, the average %RMSE differences between the fitted and the extrapolated models is 3.87%. Dg, Do, Ho, V, and W estimations for 2011 models have higher %RMSE than the one for models extrapolated to 2016. However, N and G models show higher %RMSE for the 2016 extrapolated ones.

^{2}ranges from 0.55 to 0.92 within the different stand attributes. These models also show good temporal transferability, being the average %RMSE differences between the fitted and the extrapolated model 5.85%, even lower than the models fitted in 2011 and extrapolated to 2016. All the models fitted in 2016 for the analyzed stand attributes present lower RMSE than the ones extrapolated to 2011.

## 4. Discussion

^{−2}) showed generally higher accuracy than 2011 ones (0.64 points m

^{−2}). However, no statistically significant differences were found between the best-fitted models for each year. In agreement with Cao et al. [9], point density may influence model performance but did not significantly affect the estimations of forest attributes as point clouds has a consistent vertical pattern. According to Hudak et al. [27], the relatively large size of the sample plots is considered sufficient for generating canopy height metrics. Thus, the results confirm, as other previous studies based on low-density ALS from the Spanish National Plan for Aerial Orthophotography data (i.e., [33,36,37,38]), that this information is an accurate and economic alternative to perform forest inventories when higher point density data are not available.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**Summary of the airborne laser scanning (ALS) computed metrics including the abbreviations, classes, and macro-classes defined.

Macro-Classes | Classes | ALS Computed Metrics | Abbreviations |
---|---|---|---|

Canopy height metrics (CHM) | Lower height variables | Minimum elevation | Elev. minimum |

01th percentile of the return heights | P01 | ||

05th percentile of the return heights | P05 | ||

10th percentile of the return heights | P10 | ||

20th percentile of the return heights | P20 | ||

25th percentile of the return heights | P25 | ||

L moment 1 elevation | Elev. L1 | ||

L moment 2 elevation | Elev. L2 | ||

Mean height variables | Mean elevation | Elev. Mean | |

Mode elevation | Elev. Mode | ||

30th percentile of the return heights | P30 | ||

40th percentile of the return heights | P40 | ||

50th percentile of the return heights | P50 | ||

60th percentile of the return heights | P60 | ||

70th percentile of the return heights | P70 | ||

L moment 3 elevation | Elev. L3 | ||

Elevation quadratic mean | Elev. SQRT mean SQ | ||

Elevation cubic mean | Elev. CUR mean CUBE | ||

Higher height variables | 75th percentile of the return heights | P75 | |

80th percentile of the return heights | P80 | ||

90th percentile of the return heights | P90 | ||

95th percentile of the return heights | P95 | ||

99th percentile of the return heights | P99 | ||

Maximum elevation | Elev. maximum | ||

L moment 4 elevation | Elev. L4 | ||

Canopy height variability metrics (CHVM) | Variability | Standard deviation of point heights distribution | Elev. SD |

Variance of point heights distribution | Elev. Variance | ||

Coefficient of variation of point heights distribution | Elev. CV | ||

Skewness of point heights distribution | Elev. Skewness | ||

kurtosis of point heights distribution | Elev. Kurtosis | ||

Interquartile distance of point heights distribution | Elev. IQ | ||

Average Absolute Deviation of point heights distribution | Elev. AAD | ||

Variability L moment | L moment coefficient of variation of point heights distribution | Elev. LCV | |

L moment skewness of point heights distribution | Elev. Lskewness | ||

L moment kurtosis of point heights distribution | Elev. Lkurtosis | ||

Canopy density metrics (CDM) | % first, % all returns, canopy relief ratio | percentage of first returns above the 2.00 | % first ret. above 2.00 |

percentage of all returns above the 2.00 | % all ret. above 2.00 | ||

percentage of first returns above the mean | % first ret. above mean | ||

percentage of first returns above the mode | % first ret. above mode | ||

percentage of all returns above the mean | % all ret. above mean | ||

percentage of all returns above the mode | % all ret. above mode | ||

Canopy relief ratio | CRR | ||

All returns Total returns-1 | All returns above 2.00 divided by the total first returns × 100 | (All ret. above 2.00)/(total first ret.) × 100 | |

All returns above mean divided by the total first returns × 100 | (All ret. above mean)/(total first ret.) × 100 | ||

All returns above mode divided by the total first returns × 100 | (All ret. above mode)/(total first ret.) × 100 |

**Table A2.**Summary of the N models using 2011 ALS data. Validation results in terms of RMSE (stems ha

^{−1}), %RMSE, and bias (stems ha

^{−1}) and R

^{2}. SM refers to selection method; Step. stands for Stepwise both and forward; SVMr. refers to support vector machine with radial kernel; SVM l. refers to support vector machine with linear kernel; ret. refers to returns.

Fitting Phase | Validation | ||||||||
---|---|---|---|---|---|---|---|---|---|

ALS Metrics | Model | SM | RMSE | % RMSE | Bias | RMSE | % RMSE | Bias | R^{2} |

P90 + (All ret. above mean)/(total first ret.) × 100 | MLR | Step. | 347.22 | 49.08 | 0.00 | 350.67 | 49.57 | 8.76 | 0.53 |

Elev. L2 + Elev. Variance + (All ret. above 2.00)/(total first ret.) × 100 | MDL | ASSs | 235.89 | 33.34 | −0.83 | 292.37 | 41.33 | −1.48 | 0.68 |

P99 + Elev. IQ + % first ret. above 2.00 | LWLR | Rho | 205.80 | 29.09 | −9.79 | 310.97 | 43.96 | −11.39 | 0.65 |

P99 + Elev. IQ + % first ret. above 2.00 | SVMr | rho | 257.09 | 36.34 | 28.81 | 272.76 | 38.55 | 26.99 | 0.72 |

Elev. L2 + Elev. Variance + (All ret. above 2.00)/(total first ret.) × 100 | SVMl | ASSs | 319.34 | 45.14 | 60.68 | 309.56 | 43.76 | 64.83 | 0.65 |

P99 + Elev. SD + % first ret. above 2.00 | RF | rho | 151.86 | 21.46 | 1.91 | 303.56 | 42.91 | 6.91 | 0.66 |

**Table A3.**Summary of the N models using 2016 ALS data. Validation results in terms of RMSE (stems ha

^{−1}), %RMSE, and bias (stems ha

^{−1}) and R

^{2}. SM refers to selection method; Step. stands for Stepwise both and forward; SVMr. refers to support vector machine with radial kernel; SVM l. refers to support vector machine with linear kernel; ret. refers to returns.

Fitting Phase | Validation | ||||||||
---|---|---|---|---|---|---|---|---|---|

ALS Metrics | Model | SM | RMSE | % RMSE | Bias | RMSE | % RMSE | Bias | R^{2} |

Elev. mean + Elev. L kurtosis + Canopy relief ratio | MLR | Step. | 358.84 | 51.47 | 0.00 | 363.62 | 52.15 | 11.57 | 0.45 |

Elev. maximum + Elev. L kurtosis + % first ret. above 2.00 | MDL | LASSO | 243.13 | 34.87 | 1.14 | 322.89 | 46.31 | 8.15 | 0.61 |

Elev. maximum + Elev. L kurtosis + % first ret. above 2.00 | LWLR | LASSO | 204.63 | 29.35 | 4.55 | 333.20 | 47.79 | 11.06 | 0.57 |

Elev. maximum + Elev. L kurtosis + % first ret. above 2.00 | SVMr | LASSO | 250.87 | 35.98 | 13.95 | 278.58 | 39.96 | 11.83 | 0.67 |

Elev. maximum + Elev. L kurtosis + % first ret. above 2.00 | SVMl | LASSO | 322.11 | 46.20 | 29.31 | 313.41 | 44.95 | 36.04 | 0.59 |

Elev. maximum + Elev. L kurtosis + % first ret. above 2.00 | RF | LASSO | 159.15 | 22.83 | −1.71 | 302.57 | 43.40 | −10.81 | 0.60 |

**Table A4.**Summary of the G models using 2011 ALS data. Validation results in terms of RMSE (m

^{2}ha

^{−1}), %RMSE, and bias (m

^{2}ha

^{−1}) and R

^{2}. SM refers to selection method; Step. stands for Stepwise both and forward; SVMr. refers to support vector machine with radial kernel; SVM l. refers to support vector machine with linear kernel; ret. refers to returns.

Fitting Phase | Validation | ||||||||
---|---|---|---|---|---|---|---|---|---|

ALS Metrics | Model | SM | RMSE | % RMSE | Bias | RMSE | % RMSE | Bias | R^{2} |

Elev. minimum + Elev. Kurtosis + (All ret. above mode)/(total first ret.) × 100 | MLR | rho | 5.80 | 29.80 | 0.00 | 6.01 | 30.89 | 0.19 | 0.64 |

P10 + % first ret. above 2.00 | MDL | rho | 4.61 | 23.69 | 0.21 | 5.23 | 26.85 | 0.38 | 0.74 |

P05 + % first ret. above mean | LWLR | ASSe | 4.07 | 20.92 | 0.01 | 5.53 | 28.42 | 0.12 | 0.70 |

Elev. minimum + Elev. Kurtosis + (All ret. above mode)/(total first ret.) × 100 | SVMr | ASSs | 4.43 | 22.77 | −0.10 | 4.77 | 24.51 | −0.10 | 0.77 |

Elev. minimum + Elev. Kurtosis + (All ret. above mode)/(total first ret.) × 100 | SVMl | ASSs | 4.85 | 24.92 | 0.10 | 4.87 | 25.05 | 0.05 | 0.75 |

P10 + % first ret. above 2.00 | RF | rho | 2.61 | 13.41 | 0.02 | 5.19 | 26.69 | 0.06 | 0.73 |

**Table A5.**Summary of the G models using 2016 ALS data. Validation results in terms of RMSE (m

^{2}ha

^{−1}), %RMSE, and bias (m

^{2}ha

^{−1}) and R

^{2}. SM refers to selection method; Step. stands for Stepwise both and forward; SVMr. refers to support vector machine with radial kernel; SVM l. refers to support vector machine with linear kernel; ret. refers to returns.

Fitting Phase | Validation | ||||||||
---|---|---|---|---|---|---|---|---|---|

ALS Metrics | Model | SM | RMSE | % RMSE | Bias | RMSE | % RMSE | Bias | R^{2} |

Elev. minimum +% all ret. above mode | MLR | rho | 9.27 | 42.11 | 0.00 | 9.19 | 41.76 | 0.21 | 0.15 |

P75 + Elev. CUR mean CUBE + (All ret. above 2.00)/(total first ret.) × 100 | MDL | ASSe | 3.65 | 16.57 | 0.19 | 4.43 | 20.11 | 0.12 | 0.82 |

P75 + Elev. CUR mean CUBE + (All ret. above 2.00)/(total first ret.) × 100 | LWLR | ASSe | 2.84 | 12.93 | 0.01 | 5.05 | 22.94 | −0.10 | 0.77 |

P75 + Elev. CUR mean CUBE + (All ret. above 2.00)/(total first ret.) × 100 | SVMr | ASSe | 3.88 | 17.61 | 0.41 | 4.14 | 18.80 | 0.30 | 0.84 |

P75 + Elev. CUR mean CUBE + (All ret. above 2.00)/(total first ret.) × 100 | SVMl | ASSe | 4.38 | 19.89 | 0.44 | 4.43 | 20.12 | 0.35 | 0.81 |

P10 + Elev. minimum + % first ret. above mean | RF | ASSf | 2.32 | 10.56 | 0.08 | 4.64 | 21.06 | 0.37 | 0.81 |

**Table A6.**Summary of the Dg models using 2011 ALS data. Validation results in terms of RMSE (cm), %RMSE, and bias (cm) and R

^{2}. SM refers to selection method; Step. stands for Stepwise both and forward; SVMr. refers to Support Vector Machine with radial kernel; SVM l. refers to Support Vector Machine with linear kernel; ret. refers to returns.

Fitting Phase | Validation | ||||||||
---|---|---|---|---|---|---|---|---|---|

ALS Metrics | Model | SM | RMSE | % RMSE | Bias | RMSE | % RMSE | Bias | R^{2} |

P90 + % first ret. above mean | MLR | rho | 3.80 | 18.44 | 0.00 | 3.84 | 18.60 | −0.03 | 0.77 |

P90 + (All ret. above 2.00)/(total first ret.) × 100 | MDL | ASSs | 3.30 | 15.97 | 0.16 | 3.78 | 18.34 | 0.00 | 0.78 |

P90 + (All ret. above 2.00)/(total first ret.) × 100 | LWLR | ASSs | 2.98 | 14.46 | −0.02 | 3.75 | 18.19 | −0.22 | 0.78 |

P90 + Elev. Std.dev + % first ret. above mean | SVMr | rho | 3.38 | 16.38 | 0.19 | 3.56 | 17.25 | 0.06 | 0.81 |

P90 + Elev. Std.dev + % first ret. above mean | SVMl | rho | 3.76 | 18.24 | 0.08 | 3.88 | 18.80 | −0.06 | 0.78 |

P90 + Elev. Std.dev + (All ret. above mean)/(total first ret.) × 100 | RF | rho | 1.89 | 9.17 | −0.02 | 3.75 | 18.18 | −0.04 | 0.79 |

**Table A7.**Summary of the Dg models using 2016 ALS data. Validation results in terms of RMSE (cm), %RMSE, and bias (cm) and R

^{2}. SM refers to selection method; Step. stands for Stepwise both and forward; SVMr. refers to Support Vector Machine with radial kernel; SVM l. refers to Support Vector Machine with linear kernel; ret. refers to returns.

Fitting Phase | Validation | ||||||||
---|---|---|---|---|---|---|---|---|---|

ALS Metrics | Model | SM | RMSE | % RMSE | Bias | RMSE | % RMSE | Bias | R^{2} |

P90 + Elev. LCV + (All ret. above mean)/(total first ret.) × 100 | MLR | Step. | 3.48 | 15.53 | 0.00 | 3.63 | 16.22 | −0.07 | 0.82 |

Elev. maximum + Elev. IQ + (All ret. above 2.00)/(total first ret.) × 100 | MDL | ASSf | 3.12 | 13.93 | 0.23 | 3.71 | 16.58 | 0.21 | 0.82 |

P90 + Elev. LCV + (All ret. above mean)/(total first ret.) × 100 | LWLR | Step. | 2.59 | 11.58 | −0.03 | 3.91 | 17.48 | −0.04 | 0.80 |

Elev. maximum + Elev. IQ + (All ret. above 2.00)/(total first ret.) × 100 | SVMr | ASSf | 3.03 | 13.53 | 0.21 | 3.42 | 15.28 | 0.11 | 0.85 |

P90 + Elev. mode + % first ret. above mode | SVMl | ASSs | 3.45 | 15.40 | 0.20 | 3.57 | 15.95 | 0.11 | 0.83 |

P90 + Elev. LCV + (All ret. above mean)/(total first ret.) × 100 | RF | rho | 1.65 | 7.39 | 0.01 | 3.59 | 16.05 | 0.05 | 0.82 |

**Table A8.**Summary of the Do models using 2011 ALS data. Validation results in terms of RMSE (cm), %RMSE, and bias (cm) and R

^{2}. SM refers to selection method; Step. stands for Stepwise both and forward; SVMr. refers to Support Vector Machine with radial kernel; SVM l. refers to Support Vector Machine with linear kernel; ret. refers to returns.

Fitting Phase | Validation | ||||||||
---|---|---|---|---|---|---|---|---|---|

ALS Metrics | Model | SM | RMSE | % RMSE | Bias | RMSE | % RMSE | Bias | R^{2} |

Elev. skewness + Elev. Lkurtosis + P25 | MLR | rho | 5.34 | 20.17 | 0.00 | 5.42 | 20.47 | 0.07 | 0.62 |

P90+ (All ret. above 2.00)/(total first ret.) × 100 | MDL | ASSf | 3.99 | 15.07 | 0.10 | 4.27 | 16.12 | 0.11 | 0.77 |

P90+ (All ret. above 2.00)/(total first ret.) × 100 | LWLR | ASSf | 3.49 | 13.17 | −0.03 | 4.29 | 16.19 | −0.05 | 0.77 |

P90+ (All ret. above 2.00)/(total first ret.) x 100 | SVMr | ASSf | 4.11 | 15.53 | 0.19 | 4.07 | 15.36 | 0.11 | 0.79 |

P90+ (All ret. above 2.00)/(total first ret.) × 100 | SVMl | ASSf | 4.24 | 16.01 | 0.22 | 4.20 | 15.85 | 0.11 | 0.78 |

P90 + % first ret. above mean | RF | rho | 2.13 | 8.04 | −0.11 | 4.38 | 16.55 | −0.36 | 0.76 |

**Table A9.**Summary of the Do models using 2016 ALS data. Validation results in terms of RMSE (cm), %RMSE, and bias (cm) and R

^{2}. SM refers to selection method; Step. stands for Stepwise both and forward; SVMr. refers to support vector machine with radial kernel; SVM l. refers to support vector machine with linear kernel; ret. refers to returns.

Fitting Phase | Validation | ||||||||
---|---|---|---|---|---|---|---|---|---|

ALS Metrics | Model | SM | RMSE | % RMSE | Bias | RMSE | % RMSE | Bias | R^{2} |

P90 + Elev. CV + (All ret. above mean)/(total first ret.) × 100 | MLR | Step. | 3.53 | 12.33 | 0.00 | 3.63 | 12.68 | −0.08 | 0.85 |

P90 + Elev. variance + Elev. L2 | MDL | ASSs | 3.26 | 11.40 | 0.18 | 3.47 | 12.13 | 0.23 | 0.86 |

P95 + Elev. CV | LWLR | ASSs | 2.88 | 10.07 | −0.03 | 3.63 | 12.70 | −0.09 | 0.84 |

P95 + Elev. CV | SVMr | ASSs | 3.25 | 11.35 | 0.40 | 3.40 | 11.89 | 0.33 | 0.87 |

Elev. Std.dev + Elev. Variance + P05 | SVMl | ASSe | 3.26 | 11.40 | 0.18 | 3.36 | 11.75 | 0.11 | 0.87 |

P95 + Elev. CV | RF | ASSs | 1.61 | 5.64 | −0.02 | 3.62 | 12.64 | 0.00 | 0.85 |

**Table A10.**Summary of the Ho models using 2011 ALS data. Validation results in terms of RMSE (m), %RMSE, and bias (m) and R

^{2}. SM refers to selection method; Step. stands for Stepwise both and forward; SVMr. refers to Support Vector Machine with radial kernel; SVM l. refers to Support Vector Machine with linear kernel; ret. refers to returns.

Fitting Phase | Validation | ||||||||
---|---|---|---|---|---|---|---|---|---|

ALS Metrics | Model | SM | RMSE | % RMSE | Bias | RMSE | % RMSE | Bias | R^{2} |

Elev. LCV + Elev. Lkurtosis + P01 | MLR | rho | 2.21 | 20.24 | 0.00 | 2.26 | 20.71 | 0.05 | 0.63 |

P90 + Elev. kurtosis | MDL | Step. | 1.24 | 11.36 | 0.10 | 1.44 | 13.18 | 0.08 | 0.85 |

P90 + Elev. skewness | LWLR | ASSs | 1.16 | 10.69 | −0.02 | 1.40 | 12.83 | 0.01 | 0.86 |

P90 + Elev. variance + % All ret. above mean | SVMr | ASSf | 1.32 | 12.11 | 0.11 | 1.34 | 12.30 | 0.09 | 0.87 |

Elev. L1 + Elev. maximum | SVMl | LASSO | 1.42 | 12.99 | 0.09 | 1.40 | 12.82 | 0.05 | 0.86 |

P90 + Canopy relief ratio | RF | Step. | 0.72 | 6.65 | −0.01 | 1.46 | 13.41 | −0.06 | 0.84 |

**Table A11.**Summary of the Ho models using 2016 ALS data. Validation results in terms of RMSE (m), %RMSE, and bias (m) and R

^{2}. SM refers to selection method; Step. stands for Stepwise both and forward; SVMr. refers to Support Vector Machine with radial kernel; SVM l. refers to Support Vector Machine with linear kernel; ret. refers to returns.

Fitting Phase | Validation | ||||||||
---|---|---|---|---|---|---|---|---|---|

ALS Metrics | Model | SM | RMSE | % RMSE | Bias | RMSE | % RMSE | Bias | R^{2} |

Elev. minimum + Elev. CV + Canopy relief ratio | MLR | rho | 2.41 | 20.90 | 0.00 | 2.52 | 21.91 | 0.01 | 0.51 |

P95 + Elev. Std.dev | MDL | ASSs | 0.92 | 7.99 | 0.07 | 0.95 | 8.27 | 0.07 | 0.93 |

P95 + Elev. variance | LWLR | ASSs | 0.79 | 6.87 | 0.02 | 0.98 | 8.48 | 0.00 | 0.93 |

P95 + Elev. Std.dev | SVMr | ASSs | 0.86 | 7.48 | 0.03 | 1.02 | 8.83 | 0.03 | 0.92 |

P90 + Elev. variance + Elev. SQRT mean SQ | SVMl | ASSb | 0.96 | 8.30 | 0.12 | 1.00 | 8.69 | 0.08 | 0.93 |

P95 + Elev. variance + (All ret. above mean)/(total first ret.) × 100 | RF | rho | 0.43 | 3.76 | −0.01 | 1.00 | 8.72 | −0.03 | 0.92 |

**Table A12.**Summary of the V models using 2011 ALS data. Validation results in terms of RMSE (m

^{3}ha

^{−1}), %RMSE, and bias (m

^{3}ha

^{−1}) and R

^{2}. SM refers to selection method; Step. stands for Stepwise both and forward; SVMr. refers to support vector machine with radial kernel; SVM l. refers to support vector machine with linear kernel; ret. refers to returns.

Fitting Phase | Validation | ||||||||
---|---|---|---|---|---|---|---|---|---|

ALS Metrics | Model | SM | RMSE | % RMSE | Bias | RMSE | % RMSE | Bias | R^{2} |

P20 + (All ret. above 2.00)/(total first ret.) × 100 | MDL | ASSs | 30.15 | 28.63 | 1.69 | 33.39 | 31.71 | 2.13 | 0.81 |

P20 + (All ret. above 2.00)/(total first ret.) × 100 | LWLR | ASSs | 25.89 | 24.58 | 0.05 | 34.09 | 32.37 | 0.24 | 0.80 |

Elev. L2 + Elev. CUR mean CUBE + % first ret. above mean | SVMr | Step. | 28.87 | 27.42 | 2.59 | 29.71 | 28.22 | 1.79 | 0.84 |

P20 + Elev. L skewness + (All ret. above mean)/(total first ret.) × 100 | SVMl | ASSs | 34.25 | 32.52 | 0.88 | 34.30 | 32.58 | 0.09 | 0.79 |

P20 + Elev. L skewness + % first ret. above 2.00 | RF | ASSs | 16.80 | 15.96 | 0.17 | 34.28 | 32.55 | −0.56 | 0.78 |

**Table A13.**Summary of the V models using 2016 ALS data. Validation results in terms of RMSE (m

^{3}ha

^{−1}), %RMSE, and bias (m

^{3}ha

^{−1}) and R

^{2}. SM refers to selection method; Step. stands for Stepwise both and forward; SVMr. refers to support vector machine with radial kernel; SVM l. refers to support vector machine with linear kernel; ret. refers to returns.

Fitting Phase | Validation | ||||||||
---|---|---|---|---|---|---|---|---|---|

ALS Metrics | Model | SM | RMSE | % RMSE | Bias | RMSE | % RMSE | Bias | R^{2} |

P75 + Elev. CUR mean CUBE + (All ret. above 2.00)/(total first ret.) × 100 | MDL | ASSe | 24.87 | 20.02 | −0.34 | 29.63 | 23.85 | −0.19 | 0.88 |

P75 + Elev. CUR mean CUBE + (All ret. above 2.00)/(total first ret.) × 100 | LWLR | ASSe | 20.26 | 16.30 | −0.08 | 31.80 | 25.59 | −0.06 | 0.85 |

P75 + Elev. CUR mean CUBE + (All ret. above 2.00)/(total first ret.) × 100 | SVMr | ASSe | 24.69 | 19.87 | 2.65 | 26.35 | 21.20 | 1.92 | 0.90 |

P75 + Elev. CUR mean CUBE + (All ret. above 2.00)/(total first ret.) × 100 | SVMl | ASSe | 30.49 | 24.54 | 2.60 | 31.14 | 25.06 | 1.48 | 0.86 |

Elev. L2 + Elev. CUR mean CUBE + % first ret. above 2.00 | RF | Step. | 15.25 | 12.27 | −0.38 | 31.73 | 25.53 | 0.32 | 0.86 |

**Table A14.**Summary of the W models using 2011 ALS data. Validation results in terms of RMSE (tons ha

^{−1}), %RMSE, and bias (tons ha

^{−1}) and R

^{2}. SM refers to selection method; Step. stands for Stepwise both and forward; SVMr. refers to support vector machine with radial kernel; SVM l. refers to support vector machine with linear kernel; ret. refers to returns.

Fitting Phase | Validation | ||||||||
---|---|---|---|---|---|---|---|---|---|

ALS Metrics | Model | SM | RMSE | % RMSE | Bias | RMSE | % RMSE | Bias | R^{2} |

Elev. L2 + Elev. CUR mean CUBE + % first ret. above 2.00 | MDL | Step. | 22.02 | 24.21 | 0.68 | 28.30 | 31.12 | 1.82 | 0.76 |

P10 + Elev. CUR mean CUBE + % first ret. above mean | LWLR | rho | 18.34 | 20.17 | 0.23 | 29.12 | 32.02 | 0.04 | 0.74 |

P10 + Elev. SQRT mean SQ + (All ret. above mean)/(total first ret.) × 100 | SVMr | rho | 23.00 | 25.29 | 0.75 | 24.29 | 26.71 | −0.03 | 0.82 |

P10 + Canopy relief ratio + (All ret. above mean)/(total first ret.) × 100 | SVMl | ASSf | 26.60 | 29.25 | 0.50 | 26.82 | 29.49 | 0.11 | 0.79 |

P10 + Elev. CUR mean CUBE + (All ret. above mean)/(total first ret.) × 100 | RF | rho | 14.39 | 15.83 | −0.05 | 29.43 | 32.36 | 0.24 | 0.75 |

**Table A15.**Summary of the W models using 2016 ALS data. Validation results in terms of RMSE (tons ha

^{−1}), %RMSE, and bias (tons ha

^{−1}) and R

^{2}. SM refers to selection method; Step. stands for Stepwise both and forward; SVMr. refers to support vector machine with radial kernel; SVM l. refers to support vector machine with linear kernel; ret. refers to returns.

Fitting Phase | Validation | ||||||||
---|---|---|---|---|---|---|---|---|---|

ALS Metrics | Model | SM | RMSE | % RMSE | Bias | RMSE | % RMSE | Bias | R^{2} |

P75 + Elev. CUR mean CUBE + (All ret. above 2.00)/(total first ret.) × 100 | MDL | ASSe | 19.66 | 18.44 | −0.64 | 23.44 | 21.98 | −0.43 | 0.88 |

P75 + Elev. CUR mean CUBE + (All ret. above 2.00)/(total first ret.) × 100 | LWLR | ASSe | 16.11 | 15.11 | −0.11 | 25.75 | 24.15 | 0.18 | 0.85 |

Elev. L2 + Elev. CUR mean CUBE + % first ret. above 2.00 | SVMr | Step. | 18.82 | 17.65 | 1.23 | 20.06 | 18.81 | 0.56 | 0.90 |

P75 + Elev. CUR mean CUBE + (All ret. above 2.00)/(total first ret.) × 100 | SVMl | ASSe | 22.78 | 21.37 | 1.65 | 23.43 | 21.98 | 0.80 | 0.87 |

P20 + Elev. CUR mean CUBE + All ret. above 2.00)/(total first ret.) × 100 | RF | Step. | 12.58 | 11.80 | 0.13 | 22.38 | 20.99 | 0.01 | 0.87 |

**Figure A1.**Scatterplot of predicted vs. observed values of the forest stand variables using the best-selected SVM with radial kernel 2011 models and 2016 extrapolated models. Dg and Do are expressed in cm; G is expressed in m

^{2}ha

^{−1}; H is expressed in m; N is expressed in stems ha

^{−1}; V is expressed in m

^{3}ha

^{−1}; W is expressed in tons ha

^{−1}.

**Figure A2.**Scatterplot of predicted vs. observed values of the forest stand variables using the best-selected SVM with radial kernel 2016 models and 2011 extrapolated models. Dg and Do are expressed in cm; G is expressed in m

^{2}ha

^{−1}; H is expressed in m; N is expressed in stems ha

^{−1}; V is expressed in m

^{3}ha

^{−1}; W is expressed in tons ha

^{−1}.

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**Figure 1.**Study area with the location of forest inventory plots. High spatial resolution orthophotography from Spanish National Plan for Aerial Orthophotography spatial data infrastructure (SDI) service is used as a backdrop.

**Figure 3.**Performance of selection methods for each forest inventory attribute by year (3A) and performance of selection techniques for each regression method without considering the year of the model (3B). Maximum number of computed models in Figure 3A was six for all the stand attributes except for volume (V) and total tree biomass (W), which have a maximum number of five models. Maximum number of models in Figure 3B is 14, seven for each year and stand attribute, for all regression methods. Rho stands for Spearman Rank; ASSs stands for All Subsect Selection Seqrep; ASSe stands for All Subsect Selection Exhaustive; ASSf stands for All Subsect Selection Forward; ASSb stands for All Subsect Selection Backward; and Step. b&f stands for Stepwise Selection Both Backward and Forward.

**Figure 4.**ALS selected metrics for estimating forest stand attributes for both 2011 and 2016 years. Maximum number of models is six for all the stand attributes except for V and W, which have a maximum number of five models.

**Figure 5.**

**%**root mean square error (RMSE) respect to the mean of the different regression methods for estimating the forest inventory attributes for 2011 (

**A**) and 2016 (

**B**).

Date of the Campaign | Field Data | Variables | Units |
---|---|---|---|

First: June to July 2013 | Green crown height Total height Dbh | Stand density (N) Basal area (G) Squared mean diameter (Dg) Dominant diameter (Do) Dominant height (Ho) Volume over bark (V) Total tree biomass (W) | stems ha^{−1}m ^{2} ha^{−1}cm cm m m ^{3} ha^{−1}tons ha ^{−1} |

Second: July to September 2014 | |||

Third: April 2016 |

Characteristics | Year 2011 | Year 2016 |
---|---|---|

Time period | January to February | September to November |

Laser scanning system | Leica ALS60 | Leica ALS80 |

Wavelength | 1,064 nm | 1064 nm |

Average flying altitude over sea level | 3,000 m | 3150 m |

Pulse repetition frequency | ~70 kHz | 176–286 kHz |

Scanning frequency | ~45 kHz | 28–59 Hz |

Maximum scan angle | 29° | 25° |

Nominal point density | 0.5 points m^{−2} | 1 points m^{−2} |

Average point density | 0.64 points m^{−2} | 1.25 points m^{−2} |

Accuracy of the point cloud (RMSEz) | ≤0.2 m | 0.09 m |

Forest Inventory Attribute | Min. | Max. | Range | Mean | Standard Deviation |
---|---|---|---|---|---|

N (stems ha^{−1}) | 99.03 | 3200.00 | 3100.97 | 715.61 | 486.54 |

G (m^{2} ha^{−1}) | 0.82 | 58.89 | 58.07 | 21.47 | 10.04 |

Dg (cm) | 9.04 | 43.52 | 34.48 | 21.67 | 8.01 |

Do (cm) | 9.21 | 47.96 | 38.76 | 27.79 | 8.73 |

Ho (m) | 4.69 | 18.90 | 14.21 | 11.32 | 3.54 |

V (m^{3} ha^{−1}) | 2.21 | 467.62 | 465.41 | 118.71 | 77.79 |

W (tons ha^{−1}) | 2.89 | 373.02 | 370.14 | 101.91 | 60.69 |

**Table 4.**Summary of the estimated field plot attributes using single-tree growth models for each year.

Inventory Attribute | Min. 2011 | Min. 2016 | Max. 2011 | Max. 2016 | Range 2011 | Range 2016 | Mean 2011 | Mean 2016 | SD 2011 | SD 2016 |
---|---|---|---|---|---|---|---|---|---|---|

N (stems ha^{−1}) | 99.03 | 99.03 | 3405.67 | 3161.81 | 3306.64 | 3062.79 | 709.64 | 699.20 | 500.86 | 481.00 |

G (m^{2} ha^{−1}) | 0.11 | 0.91 | 57.56 | 58.69 | 57.45 | 57.77 | 19.71 | 22.26 | 9.97 | 10.14 |

Dg (cm) | 3.29 | 9.55 | 41.41 | 45.05 | 38.12 | 35.50 | 20.72 | 22.45 | 7.99 | 8.40 |

Do (cm) | 3.35 | 9.72 | 45.85 | 49.19 | 42.50 | 39.47 | 26.59 | 28.72 | 8.84 | 9.09 |

Ho (m) | 4.24 | 4.90 | 18.46 | 19.08 | 14.22 | 14.17 | 10.97 | 11.58 | 3.70 | 3.60 |

V (m^{3} ha^{−1}) | 0.35 | 2.51 | 454.77 | 476.02 | 454.42 | 473.51 | 107.31 | 126.45 | 74.83 | 81.48 |

W (tons ha^{−1}) | 1.34 | 3.14 | 359.22 | 377.82 | 357.88 | 374.68 | 92.46 | 108.26 | 58.10 | 63.63 |

**Table 5.**Summary of the best-selected SVMr 2011 models and 2016 extrapolated ones. ret. refers to returns; e is extrapolated; N is stand density; G is basal area; Dg is squared mean diameter; Do is dominant diameter; Ho is dominant height; V is timber volume over bark of stem; W is total tree biomass.

Fitting Phase | Validation | |||||||
---|---|---|---|---|---|---|---|---|

Attribute | ALS Metrics | RMSE | % RMSE | Bias | RMSE | % RMSE | Bias | R^{2} |

N 2011 N 2016e | P99 + ElevIQ + % first ret. Above 2.00 | 257.09 | 36.34 | 28.81 | 272.76 | 38.55 | 26.99 | 0.72 |

265.62 | 38.10 | 17.99 | 295.83 | 42.43 | 20.49 | 0.64 | ||

G 2011 G 2016e | Elev. minimum + Elev. kurtosis + % first ret. above mean | 4.43 | 22.77 | −0.10 | 4.77 | 24.51 | −0.10 | 0.77 |

4.18 | 19.01 | 0.20 | 5.51 | 25.05 | 0.57 | 0.71 | ||

Dg 2011 Dg 2016e | P90 + Elev. SD + % first ret. above mean | 3.38 | 16.38 | 0.19 | 3.56 | 17.25 | 0.06 | 0.81 |

3.02 | 13.48 | 0.19 | 3.43 | 15.35 | 0.06 | 0.85 | ||

Do 2011 Do 2016e | P90 + (All ret. Above 2)/(total first ret) × 100 | 4.11 | 15.53 | 0.19 | 4.07 | 15.36 | 0.11 | 0.79 |

3.43 | 11.99 | 0.41 | 3.53 | 12.33 | 0.31 | 0.86 | ||

Ho 2011 Ho 2016e | P90 + Elev. variance + % all ret. above mean | 1.32 | 12.11 | 0.11 | 1.34 | 12.30 | 0.09 | 0.87 |

0.86 | 7.47 | 0.10 | 0.98 | 8.54 | 0.10 | 0.93 | ||

V 2011 V 2016e | Elev. L2 + Elev. cubic mean + % first ret. above mean | 28.87 | 27.42 | 2.59 | 29.71 | 28.22 | 1.79 | 0.84 |

25.03 | 20.15 | 3.14 | 26.00 | 20.92 | 2.64 | 0.90 | ||

W 2011 | P10 + Elev. Quadratic mean + (All ret. Above mean)/(total first ret) × 100 | 23.00 | 25.29 | 0.75 | 24.29 | 26.71 | −0.03 | 0.82 |

W 2016e | 19.63 | 18.41 | 1.80 | 21.39 | 20.06 | 1.08 | 0.89 |

**Table 6.**Summary of the best-selected SVMr 2016 models and 2011 extrapolated ones. ret. refers to returns; e is extrapolated; N is stand density; G is basal area; Dg is squared mean diameter; Do is dominant diameter; Ho is dominant height; V is timber volume over bark of stem; W is total tree biomass.

Fitting Phase | Validation | |||||||
---|---|---|---|---|---|---|---|---|

Attribute | ALS Metrics | RMSE | % RMSE | Bias | RMSE | % RMSE | Bias | R^{2} |

N 2011e | Elev. maximum + Elev. L kurtosis + % first ret. Above 2.00 | 256.69 | 36.28 | 33.73 | 340.20 | 48.09 | 49.31 | 0.55 |

N 2016 | 250.87 | 35.98 | 13.95 | 278.58 | 39.96 | 11.83 | 0.67 | |

G 2011e | P75 + Elev. CUR mean CUBE + (All ret. Above 2)/(total first ret) × 100 | 4.97 | 25.54 | 0.26 | 5.04 | 25.88 | 0.13 | 0.74 |

G 2016 | 3.88 | 17.61 | 0.41 | 4.14 | 18.80 | 0.30 | 0.84 | |

Dg 2011e | Elev. maximum + Elev. IQ + (All ret. Above 2)/(total first ret) × 100 | 3.54 | 17.14 | 0.14 | 3.77 | 18.25 | 0.00 | 0.79 |

Dg 2016 | 3.03 | 13.53 | 0.21 | 3.42 | 15.28 | 0.11 | 0.85 | |

Do 2011e | P99 + Elev. CV | 4.20 | 15.85 | 0.25 | 4.18 | 15.79 | 0.16 | 0.78 |

Do 2016 | 3.25 | 11.35 | 0.40 | 3.40 | 11.89 | 0.33 | 0.87 | |

Ho 2011e | P95 + Elev. SD | 1.32 | 12.12 | 0.03 | 1.38 | 12.64 | 0.03 | 0.86 |

Ho 2016 | 0.86 | 7.48 | 0.03 | 1.02 | 8.83 | 0.03 | 0.92 | |

V 2011e | P75 + Elev. CUR mean CUBE + (All ret. Above 2)/(total first ret) × 100 | 29.97 | 28.46 | 1.51 | 30.96 | 29.40 | 0.84 | 0.83 |

V 2016 | 24.69 | 19.87 | 2.65 | 26.35 | 21.20 | 1.92 | 0.90 | |

W 2011e | Elev. L2 + Elev. CUR mean CUBE + % first ret. Above 2.00 | 23.11 | 25.42 | 0.96 | 23.36 | 25.69 | 0.27 | 0.83 |

W 2016 | 18.82 | 17.65 | 1.23 | 20.06 | 18.81 | 0.56 | 0.90 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Domingo, D.; Alonso, R.; Lamelas, M.T.; Montealegre, A.L.; Rodríguez, F.; de la Riva, J.
Temporal Transferability of Pine Forest Attributes Modeling Using Low-Density Airborne Laser Scanning Data. *Remote Sens.* **2019**, *11*, 261.
https://doi.org/10.3390/rs11030261

**AMA Style**

Domingo D, Alonso R, Lamelas MT, Montealegre AL, Rodríguez F, de la Riva J.
Temporal Transferability of Pine Forest Attributes Modeling Using Low-Density Airborne Laser Scanning Data. *Remote Sensing*. 2019; 11(3):261.
https://doi.org/10.3390/rs11030261

**Chicago/Turabian Style**

Domingo, Darío, Rafael Alonso, María Teresa Lamelas, Antonio Luis Montealegre, Francisco Rodríguez, and Juan de la Riva.
2019. "Temporal Transferability of Pine Forest Attributes Modeling Using Low-Density Airborne Laser Scanning Data" *Remote Sensing* 11, no. 3: 261.
https://doi.org/10.3390/rs11030261